Assumption (REF ) and () respectively imply that the stochastic gradient is unbiased and has a bounded variance, and both are standard assumptions in stochastic optimization [1]}.
Assumption () states that the stochastic gradient has a bounded norm, which may seem strong especially when the objective is (unconstrained) strongly convex [2]}; however, note that Assumption (REF ) is restricted to PSD matrices,
and the original Problem (REF ) is constrained.
